Annika just answered your e-mail with this question. Here's her answer:

"Most likely, the entire trip Zurich-Interlaken will count as one transfer, not two. However, the “5 transfer card” is not one of the standard Swiss rail passes; these are listed at http://www. myswissalps.com/ swissrailpasses. I think your transfer card is a personalized product, so you can best check with your reseller and ask them how this product works."

As for your follow-up question through e-mail: yes, tickets will be checked inside the train. You can find a seat and show your tickets when requested.